How are you holding the cube? If you have it “locked” to your player, then its weight and other physical parameters will have no effect, since it is being “forced” through space. Try attaching the cube to the player using a spring constraint, this will allow it to “push” against objects in the world using natural physics. This can be tricky to setup (mostly due to poor documentation), but the results will be much better.
Also, another thing to look at to make it feel more realistic is the angular and linear damping values – I generally find these need to be higher than the defaults to keep an object from spinning out of control.